locus of incenter is a line, starting with non intersecting circles, ext. each
Source: 2009 Oral Moscow Geometry Olympiad grades 8-9 p6
September 19, 2020
geometryincentercircles
Problem Statement
Fixed two circles and , one of their external tangent and one of their internal tangent . On the line , a point is chosen, and on the line , points and are constructed so that and touch and , respectively, and the triangle contains circles and . Prove that the centers of the circles inscribed in triangles lie on one line.(P. Kozhevnikov)